document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217322>Question 217322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all the angles between 0° to 360° inclusive which satisfy the equation<BR>\n" );
document.write( "i) 2cot^2x + 5 = 7cosecx ii) 2cos^2x + 3sinx = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163888 by </B><A HREF=/tutors/aboutme.mpl?userid=chibisan><B>chibisan(131)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chibisan><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=chibisan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i)<BR>\n" );
document.write( "cot^2x = cosec^2x -1\r<BR>\n" );
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document.write( "2cot^2+5=7cosecx<BR>\n" );
document.write( "2(cosec^2x-1)+5 = 7cosecx<BR>\n" );
document.write( "2cosec^2x -2 + 5 = 7cosecx<BR>\n" );
document.write( "2cosec^2x -7cosecx +3 = 0<BR>\n" );
document.write( "(2cosecx-1)(cosecx - 3)= 0\r<BR>\n" );
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document.write( "cosecx = 1/2<BR>\n" );
document.write( "1/sinx = 1/2<BR>\n" );
document.write( "sinx = 2<BR>\n" );
document.write( "(no solution)\r<BR>\n" );
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document.write( "cosecx=3<BR>\n" );
document.write( "1/sinx = 3<BR>\n" );
document.write( "sinx =1/3<BR>\n" );
document.write( "x = 19.5° , 180 - 19.5°<BR>\n" );
document.write( "x = 19.5 , 160.5° (ans)\r<BR>\n" );
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document.write( "ii)<BR>\n" );
document.write( "2cos^2x + 3sinx = 3<BR>\n" );
document.write( "2(1-sin^2x) + 3sinx - 3=0<BR>\n" );
document.write( "-2sin^2x + 3sinx + 1= 0<BR>\n" );
document.write( "0= 2sin^2x - 3sinx + 1<BR>\n" );
document.write( "0= (2sinx- 1)(sinx - 1)\r<BR>\n" );
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document.write( "sinx = 1/2 <BR>\n" );
document.write( "x = 30° , 180 - 30°<BR>\n" );
document.write( "x = 30° , 150°\r<BR>\n" );
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document.write( "sinx =1<BR>\n" );
document.write( "x= 90°, 180°-90°<BR>\n" );
document.write( "x = 90°\r<BR>\n" );
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document.write( "x= 30° , 90° , 150° (ans) </SPAN>\n" );
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